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A242494 Decimal expansion of Sum_{k > 0} (-1)^k*log(k)^2/k. 3
0, 6, 5, 3, 7, 2, 5, 9, 2, 5, 5, 8, 8, 9, 8, 5, 9, 9, 1, 4, 6, 2, 0, 7, 3, 9, 9, 3, 8, 8, 2, 0, 1, 0, 5, 3, 2, 2, 8, 5, 8, 8, 1, 4, 9, 1, 9, 2, 9, 0, 9, 2, 0, 7, 2, 9, 7, 8, 2, 6, 6, 3, 4, 6, 0, 4, 8, 1, 8, 9, 8, 7, 3, 6, 1, 0, 4, 5, 3, 2, 9, 3, 6, 8, 6, 6, 2, 8, 9, 5, 4, 6, 4, 0, 2, 5, 6, 7, 0, 2, 4 (list; constant; graph; refs; listen; history; text; internal format)
OFFSET

0,2

REFERENCES

Steven R. Finch, Mathematical Constants, Cambridge University Press, 2003, chapter 2.21, p. 168.

LINKS

Table of n, a(n) for n=0..100.

FORMULA

sum(k>0, (-1)^k*log(k)^2/k) = -log(2)^3/3 + gamma*log(2)^2 + gamma(1)*log(4).

EXAMPLE

0.065372592558898599146207399388201...

MATHEMATICA

-Log[2]^3/3 + EulerGamma*Log[2]^2 +  StieltjesGamma[1]*Log[4] // RealDigits[#, 10, 100]& // First

PROG

(PARI) sumalt(k=1, (-1)^k*log(k)^2/k) \\ Charles R Greathouse IV, Mar 10 2016

CROSSREFS

Cf. A091812.

Sequence in context: A019686 A143304 A021157 * A193211 A195713 A306712

Adjacent sequences:  A242491 A242492 A242493 * A242495 A242496 A242497

KEYWORD

nonn,cons

AUTHOR

Jean-Fran├žois Alcover, May 16 2014

STATUS

approved

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Last modified October 18 07:40 EDT 2019. Contains 328146 sequences. (Running on oeis4.)